Expert: Paul Klarreich - 11/16/2010

Question
Milt Famey hits a line drive to center field. As he rounds
second base, he heads directly for third, running at
20ft/sec. Write an equation expressing the rate of change of
his distance from home plate as a function of his
displacement from third base. Plot the graph in a suitable
domain. How fast is this distance changing when he is
halfway to third? At third? Is the latter answer reasonable?
Explain.
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Answer
Questioner:   Andrew
Country:  United States
Category:  Calculus
Private:  No
 
Subject:  AP Calculus: Related rates, baseball diamond
Question:  Milt Famey hits a line drive to center field.

>> You are not serious -- I remember Famey.  He was a notorious pull hitter.  

As he rounds second base, he heads directly for third, running at
20ft/sec. Write an equation expressing the rate of change of
his distance from home plate as a function of his
displacement from third base. Plot the graph in a suitable
domain. How fast is this distance changing when he is
halfway to third? At third? Is the latter answer reasonable?
Explain.
.........................................

Like all R-R problems

(See

http://en.allexperts.com/q/Calculus-2063/2009/11/Related-Rates-87.htm

for many more.)

V's:
x = distance from third.
r = distance from home
z = distance from third to home.  Oh, yes, that is 90, a constant.

R's:
dx/dt = -20
dr/dt TO BE FOUND.

Relation:

x^2 + 90^2 = r^2

Diff:

2x dx/dt = 2r dr/dt

x dx/dt = r dr/dt

        x dx/dt
dr/dt = ---------
          r

and you can find r from the relation.

I think you can handle the rest.